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A question on groups having a subgroup which fixes a vector in every irreducible representat...

Given a finite group $G$, I am interested in finding a non-trivial proper subgroup $H$ of $G$ such that $\mathrm{Ind}_H^G\mathbf{1}$ contains all the irreducible representations of $G$, that is, perm …
Soumyadip Sarkar's user avatar